It has been a long held belief of many that repetition is the key to mastery of a subject. Also known as the "practice makes perfect" theory, the more frequently a problem is presented to a student, the more successful the student will be at solving the problem. This can be especially true in the area of grade school mathematics. Where mathematical equations can initially be a conglomeration of meaningless numbers to students, their repeated exposure to problems assist in their ability to eventually solve a given problem correctly.
As a result, a plethora of computer-based programs have been created which are premised on the "practice makes perfect" theory. Using a variety of audio and visual mechanisms, the underlying approach of these programs has been to force feed problems to a student, and to repeat any problems that a student misses. However, since each student possesses different areas of difficulty, and learns at a different pace, mere presentation and repetition of a problem is not always effective. For instance, if a student misses problem A once and problem B five times, random repetition will dictate that problem A has an equal probability of being selected as problem B. This can be ineffective because it does not focus a student's attention on a particular problem that he or she is having the greatest difficulty with, that is, problem B, and therefore does not consider the student's actual performance in selecting problems.
One solution is to repeat a missed problem in variable intervals according to the student's performance, where one interval is measured by the presentation of one problem. For example, if a student misses problem A, it will be repeated in a preconfigured interval that is increased if the student correctly answers the problem on the next presentation, or decreased if the student incorrectly answers the problem on the next presentation. If the preconfigured interval is one, then the first sequence of problem presentation following the first time that problem A is missed is:
Repetition 1: PA0 Repetition 2: PA0 Repetition 3:
problem B (INTERVAL 1) PA1 problem A PA1 problem B (INTERVAL 1) PA1 problem C (INTERVAL 2) PA1 problem A PA1 problem B (INTERVAL 1) PA1 problem C (INTERVAL 2) PA1 problem D (INTERVAL 3) PA1 problem A
If the student correctly answers problem A in Repetition 1, then the interval increases to two, for example, and the sequence of problem presentation following Repetition 1 becomes:
If the student correctly answers problem A in Repetition 2, then the interval increases to three, for example, and the sequence of problem presentation following Repetition 2 becomes:
If the student answers problem A in any repetition incorrectly, then the previous repetition is repeated, or Repetition 1 if there is no previous repetition. Once the student correctly answers the missed problem for all repetitions, up to a preconfigured maximum number of repetitions, it is not repeated in preconfigured intervals until it is missed again. There can, of course, be intervening repetitions for problems presented during the intervals, the details of which are not discussed herewith. (See expired U.S. Pat. No. 4,193,210 of Turnquist.)
Although this solution presents problem repetition commensurate with the student's performance, it is vulnerable to some degree of predictability as to subsequent presentation of problems because problem presentation under this method is methodical. In other words, if there are 5 problems, A, B, C, D, and E, and a student misses problem A, and then problem B, the missed problems will necessarily be repeated in sequential fashion. Even though there are interval problems to distance the repetition of missed problems, the repetition is nevertheless a sequential event. A need exists, therefore, for an apparatus and a method of selecting a problem that is adapted to a student's performance, such that a problem missed more frequently has a higher probability of being repeated more frequently than a problem missed less frequently, without the predictability that such a problem will necessarily be repeated on any given problem selection.